Variational Quantum Algorithms as Hybrid Control Systems
An interactive thesis exploring optimization dynamics in variational quantum algorithms—separating the quantum substrate from the classical controller.
Chapters
Why VQAs should be analyzed as hybrid control systems, and what this lens explains.
Parameterized states, observables, measurement, and how the objective landscape is induced.
Mapping circuits + estimators + optimizers into a closed-loop system model.
Why non-gradient dynamics matter under noise, nonconvexity, and sampling.
Damped-oscillator swarm dynamics, periodic-boundary handling, and benchmarks on H₂ and LiH.
A quadratic penalty that conditions the classical landscape, and how far the benefit survives realistic noise.
What this viewpoint changes: benchmarking, design rules, and future directions.
Appendices
Jordan–Wigner and Bravyi–Kitaev mappings, Pauli decomposition, qubit requirements.
Pauli term grouping, commuting cliques, shot budgets, and estimator variance.
Statevector vs shot-based simulation, depolarizing noise, and how noise enters the optimization loop.
The curvature matrix, why ansatz redundancy flattens part of its spectrum, and how the penalty conditions it.